I bet many people would care, but they would not persistently & vocally voice their discomfort for fear of retribution/confrontation.
> how should we Italians feel about being always portrayed as "pizza, mafia, gobbledygook mamma mia"?
In popular media? Complain to the broadcaster/studio/publisher, support organisations like the Italic Institute of America to do this on your behalf.
Why should you do that? Because you think that the stereotypes unfairly prejudice Italians who may be denied opportunities in those countries.